Question

cam divided $(x^4 + 3x^2 - 4x - 2)$ by factor of $(x - 2)$ using synthetic division. his work is shown above. which best describes his mistake? cam wrote the remainder incorrectly. cam did not use a zero place holder for the $x^3$ term. cam added instead of subtracting the rows. cam should have used -2 as his division since the factor was $x - 2$.

Explanation:

Step1: Identify polynomial coefficients

The polynomial is $x^4 + 3x^2 - 4x - 2$, which can be rewritten as $x^4 + 0x^3 + 3x^2 - 4x - 2$. Its coefficients are $1, 0, 3, -4, -2$.

Step2: Check Cam's setup

Cam used coefficients $1, 3, -4, -2$, omitting the $0$ for the $x^3$ term.

Step3: Evaluate other options

• Option A: The remainder calculation follows his incorrect setup, so this is wrong.
• Option C: Synthetic division uses addition, so this is wrong.
• Option D: For factor $(x-2)$, we use $2$ in synthetic division, so this is wrong.

Answer:

B. Cam did not use a zero place holder for the $x^3$ term.